Is the narrator a round or flat character? Give a quote to support your answer.

In James Baldwin's short story about two brothers who finally come to understand one another through the medium of music, the brother who is the narrator is a round character. That is, he is a character who experiences an essential change in attitude.
The brother who acts as narrator in "Sonny's Blues" has been alienated from Sonny for years because he has become a drug addict. When the narrator reads in the newspaper about Sonny's arrest for heroin, he becomes perturbed, reminded of his students in Harlem who also are growing up in "the killing fields" with limited prospects in life. After encountering a drug addict who is an old acquaintance of Sonny's, the narrator feels guilty about failing in his promise to his mother to watch out for his brother. So, he decides to find Sonny and bring him back home to Harlem. After the narrator locates his brother, Sonny agrees to come home with the narrator; nevertheless, the narrator is concerned that Sonny may still be using drugs.
One day when Sonny is out, the brother is tempted to check and see if Sonny has brought drugs into the home. However, when he hears music outside where some people are holding a street revival, he goes to the window.

As the singing filled the air, the watching, listening faces underwent a change...the music seemed to soothe a poison out of them; and time seemed nearly to fall from the sullen, belligerent, battered faces....

Sonny stands on the sidewalk, watching and listening. Then, with his slow, loping, and musical walk, Sonny crosses the street and enters the brother's apartment. The brother and Sonny talk about these street singers. Then, Sonny invites his brother to listen to him that night because he is going to play "at a joint in the Village."
It is at this nightclub that the narrator undergoes an epiphany. While he listens to the musicians, he realizes that "music makes something real for them." As Sonny joins in on the piano with the other musicians, the brother understands that "there was no battle on his face now." Sonny makes the musical piece his own through improvisation.

He had made it his; that long line, of which we knew only Mama and Daddy. And he was giving it back, as everything must be given back, so that, passing through death, it can live forever.

The narrator's past comes back to him. He sees his parents' faces; he sees the moonlit road where his uncle was killed. He sees again his little girl who died of polio. He knows suffering, he feels the suffering of Sonny, and he is all too aware that "the world waited outside, as hungry as a tiger, and that trouble stretched above us, longer than the sky."
It is in this nightclub as he listens to Sonny pour his soul into the ivory and ebony of the piano keys that the narrator finally understands his brother's suffering. The cup of Scotch and milk placed on Sonny's piano becomes symbolic of "the very cup of trembling." This moment is, indeed, spiritual as the brother is, at last, connected to his brother, Sonny. Both Sonny and he have suffered; in this suffering they are united.